How Probability Distributions Felled the Case for the Beneficial Effects of Income Inequality

Music City Center 

This paper examines some of the ways that probability distributions (such as the exponential, lognormal, and Pareto families) advance knowledge across disciplines and topical domains, focusing on the social sciences. The paper begins with the titular case – how probability distributions expanded the meaning of inequality from inequality between persons to inequality between subgroups, thereby undermining the case for the beneficial effects of income inequality. For while it may have been straightforward to defend the beneficial incentive effects of inequality between persons it is a different matter entirely to defend inequality between subgroups. One key element in this evolution was the increasing use of probability distributions (such as the exponential, lognormal, and Pareto families), which made visible and inescapable a tight link between the two types of inequality. The paper then turns to four further applications in which probability distributions reveal new aspects of sociobehavioral phenomena, showing how inequality in ordinal characteristics differs from inequality in cardinal characteristics (for example, the Gini coefficient is constant), assessing new candidates for inequality measures (illustrating with the P90/P10 ratio and its sibling quantile ratios), showing how theoretical predictions differ across different distributional families (for example, for proportions integrationist and segregationist), and discerning in empirical data around the world how people form ideas of the just job income for themselves (for example, whether they fix on a constant or a multiple or compare to everyone).

Keywords: Inequality between persons and inequality between subgroups; inequality measurement; probability distributions; amounts and ranks; justice, status, power; just reward scenarios; Coleman Box

inequality between persons and inequality between subgroups

inequality measurement

probability distributions

amounts and ranks

comparison, status, power

just reward scenarios 

Social Statistics Section